. The Bell System technical journal . , J-J / \ ^ /I -^c \ / \ 1^^^ Fig. 2—Tchebycheff poh-nomials. NETWORK SYNTHESIS ()17 is especially appropriate for general network applications, because theodd ordered polynomials contribute to the imaginary parts of complexnetwork functions—such as ijS in a -\- ib.\ It is apparent from (3) that the Tchebycheff polynomials becomesimply Fourier harmonics, if they are plotted against a distorted fre-quency scale—that is, against 0. This means that they must be ortho-gonal, over that particular range of frequencies which corresponds toreal values of 4>. Fr
. The Bell System technical journal . , J-J / \ ^ /I -^c \ / \ 1^^^ Fig. 2—Tchebycheff poh-nomials. NETWORK SYNTHESIS ()17 is especially appropriate for general network applications, because theodd ordered polynomials contribute to the imaginary parts of complexnetwork functions—such as ijS in a -\- ib.\ It is apparent from (3) that the Tchebycheff polynomials becomesimply Fourier harmonics, if they are plotted against a distorted fre-quency scale—that is, against 0. This means that they must be ortho-gonal, over that particular range of frequencies which corresponds toreal values of 4>. From the relation between 4> and co, it is clear that real\alues of (/) cover the frequency interval between — Wc and -\-Uc , whichis our useful interval. In other words, the interval of orthogonality coin-cides witii the useful frec}uency inter\al. The corresponding interval ofp is of course p = —iojc to -\-iuc . If a given fiuiction is plotted against <^, instead of w, it may be ex-panded in a Fourier series. Each ter
Size: 1782px × 1402px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
